Does light orbit the universe?

Question

Or rather, does mass-less particles orbit the matter in the universe due to the infinite range of gravity? And if yes, in what shape are they orbiting? A ring as on Saturn? Maybe a whirlpool due to the expansion of space? A full shell?

Answer 1

I illustrate in this post how a cosmology with a constant density of energy in the vacuum will in fact accelerate outwards. This will not permit the orbiting of particles or light on a large scale.

There is the Godel solution that has closed timelike curves. This is different than an orbit, but a case where geodesics have a time parameter that is topologically a circle. The anti-de Sitter spacetime is similar in that $AdS_n$ has topology $\mathbb R^{n-1}\times\mathbb S^1$. Here the spatial surface is the $\mathbb R^{n-1}$ and time is $S^1$. This spacetime is different from the spacetime that approximates what we observe that is $\mathbb S^{n-1}\times\mathbb R$. However, it is possible that our observable cosmology emerges from and anti-de Sitter spacetime. Maybe the inflationary spacetime that spins off cosmology at a lower vacuum energy is an anti-de Sitter spacetime.